Existence of multiple equilibrium points in global attractor for damped wave equation
| Autor: | Chang Zhang, Fengjuan Meng, Cuncai Liu |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Equilibrium point
Lyapunov function Algebra and Number Theory Partial differential equation Dynamical systems theory 010102 general mathematics Mathematical analysis lcsh:QA299.6-433 Equilibrium points lcsh:Analysis Lyapunov functional Wave equation 01 natural sciences Global attractor 010101 applied mathematics symbols.namesake Ordinary differential equation Saddle point Attractor symbols Z 2 $Z_{2}$ index 0101 mathematics Analysis Mathematics |
| Zdroj: | Boundary Value Problems, Vol 2019, Iss 1, Pp 1-9 (2019) |
| ISSN: | 1687-2770 |
| DOI: | 10.1186/s13661-019-1123-2 |
| Popis: | This paper is a continuation of Meng and Zhong in (Discrete Contin. Dyn. Syst., Ser. B 19:217–230, 2014). We go on studying the property of the global attractor for some damped wave equation with critical exponent. The difference between this paper and Meng and Zhong in (Discrete Contin. Dyn. Syst., Ser. B 19:217–230, 2014) is that the origin is not a local minimum point but rather a saddle point of the Lyapunov function F for the symmetric dynamical systems. Using the abstract result established in Zhang et al. in (Nonlinear Anal., Real World Appl. 36:44–55, 2017), we prove the existence of multiple equilibrium points in the global attractor for some wave equations under some suitable assumptions in the case that the origin is an unstable equilibrium point. |
| Databáze: | OpenAIRE |
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